12,222 research outputs found

    Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

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    Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure

    A local potential for the Weyl tensor in all dimensions

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    In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.Comment: 7 pages; Late

    The Vertical Structure of Planet-induced Gaps in Proto-Planetary Discs

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    Giant planets embedded in circumstellar discs are expected to open gaps in these discs. We examine the vertical structure of the gap edges. We find that the planet excites spiral arms with significant (Mach number of a half) vertical motion of the gas, and discuss the implications of these motions. In particular, the spiral arms will induce strong vertical stirring of the dust, making the edge appeared `puffed up' relative to the bulk of the disc. Infra-red observations (sensitive to dust) would be dominated by the light from the thick inner edge of the disc. Sub-millimetre observations (sensitive to gas velocities) would appear to be hot in `turbulent' motions (actually the ordered motion caused by the passage of the spiral arms), but cold in chemistry. Resolved sub-millimetre maps of circumstellar discs might even be able to detect the spiral arms directly.Comment: Revision adds new data, and corrects physical intepretatio

    Irreducible Killing Tensors from Third Rank Killing-Yano Tensors

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    We investigate higher rank Killing-Yano tensors showing that third rank Killing-Yano tensors are not always trivial objects being possible to construct irreducible Killing tensors from them. We give as an example the Kimura IIC metric were from two rank Killing-Yano tensors we obtain a reducible Killing tensor and from third rank Killing-Yano tensors we obtain three Killing tensors, one reducible and two irreducible.Comment: 10 page

    Exploring Communication Tendencies of Program Facilitators

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    Audience analysis is a critical skill to forge relationships and develop effective communications. Programs provided by the Cooperative Extension Service must be aware of external and internal audiences to provide relevant information and evoke impacts. Berlo’s (1960) Source-Message-Channel-Receiver Model of Communications guided this formative evaluation of Extension staff, and horse 4-H club volunteer leaders (program facilitators) to expose internal communication tendencies in Arkansas. Findings identified that program facilitators seek horse-related information from a variety of sources, most frequently relying on personal connections and least frequently seeking Extension sources. Program facilitators share a variety of messages and most frequently relay information about deadlines to club members. Messages about recruitment and fundraising were shared least often. Program facilitators described utilizing a variety of personal and electronic channels to share messages with the greatest frequency for in-person communications. Incoming channels were less diverse than outgoing channels and primarily featured email, which program facilitators preferred. Program facilitators are primarily female, aged in their thirties, described lifetime involvement with 4-H and the horse industry, and most frequently reported having less than five years’ experience in their current position. The ground-level perspective of facilitators’ demographics and communication tendencies was evident in results of this study. In application, practitioners must continue to actively seek relationships with audiences, remain cognizant of communication factors, and provide accurate messaging through preferred channels

    Feasibility of vegetable production in the Mad River Valley of Ohio

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    Socially-mediated arousal and contagion within domestic chick broods

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    Emotional contagion – an underpinning valenced feature of empathy – is made up of simpler, potentially dissociable social processes which can include socially-mediated arousal and behavioural/physiological contagion. Previous studies of emotional contagion have often conflated these processes rather than examining their independent contribution to empathic response. We measured socially-mediated arousal and contagion in 9-week old domestic chicks (n = 19 broods), who were unrelated but raised together from hatching. Pairs of observer chicks were exposed to two conditions in a counterbalanced order: air puff to conspecifics (AP) (during which an air puff was applied to three conspecifics at 30 s intervals) and control with noise of air puff (C) (during which the air puff was directed away from the apparatus at 30 s intervals). Behaviour and surface eye temperature of subjects and observers were measured throughout a 10-min pre-treatment and 10-min treatment period. Subjects and observers responded to AP with increased freezing, and reduced preening and ground pecking. Subjects and observers also showed reduced surface eye temperature - indicative of stress-induced hyperthermia. Subject-Observer behaviour was highly correlated within broods during both C and AP conditions, but with higher overall synchrony during AP. We demonstrate the co-occurrence of socially-mediated behavioural and physiological arousal and contagion; component features of emotional contagion
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